50 citations · 202 across the 30 of their papers we have counts for
6 papers · 1 filter
Algebraic structure of stochastic expansions and efficient simulation
Kurusch Ebrahimi-Fard, Alexander Lundervold, Simon J. A. Malham +2
We investigate the algebraic structure underlying the stochastic Taylor solution expansion for stochastic differential systems.Our motivation is to construct efficient integrators.…
An introduction to SDE simulation
Simon J. A. Malham, Anke Wiese
We outline the basic ideas and techniques underpinning the simulation of stochastic differential equations. In particular we focus on strong simulation and its context. We also pro…
Grassmannian spectral shooting
Veerle Ledoux, Simon J. A. Malham, Vera Thummler
We present a new numerical method for computing the pure-point spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting a…
Efficient strong integrators for linear stochastic systems
Gabriel Lord, Simon J. A. Malham, Anke Wiese
We present numerical schemes for the strong solution of linear stochastic differential equations driven by an arbitrary number of Wiener processes. These schemes are based on the N…
Stochastic Lie group integrators
Simon J. A. Malham, Anke Wiese
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold.…
Evaluating the Evans function: Order reduction in numerical methods
Simon Malham, Jitse Niesen
We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans funct…